“Boundary conditions for first-order hyperbolic relaxation systems”
Mercoledì 25 Marzo 2026, ore 13:30 - Aula 2AB40 - Yizhou Zhou (IGPM RWTH Aachen University))
Abstract
The first-order hyperbolic relaxation system is a class of time-dependent partial differential equations which model various non-equilibrium phenomena. For such systems, the main interest is to understand the zero relaxation limit. The initial-value problem for the relaxation system has been well-developed and a systematical framework has been built. However, the initial-boundary value problem of the relaxation system is still in the developing stage. In this talk, I will first introduce the theory of boundary conditions for general relaxation systems. Then I will present the recent results for the initial-boundary-value problem with characteristic boundaries. Specifically, we redefine a characteristic Generalized Kreiss condition (GKC) which is essentially necessary to have a well-behaved relaxation limit. Under this characteristic GKC and a Shizuta-Kawashima-like condition, we derive reduced boundary conditions for the relaxation limit solving the corresponding equilibrium systems and justify the validity.
